Poisson transforms on right-angled Artin monoids
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915220829503488 |
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| author | Li, Boyu |
| author_facet | Li, Boyu |
| contents | We introduce the notion of the weak Brehmer's condition and prove that the Cauchy transform for a representation of a right-angled Artin monoid is bounded under such conditions. As a result, we obtain the Poisson transform and $*$-regular dilation for a family of operators that satisfies the weak Brehmer's condition and the property (P). This generalizes Popescu's notion of Cauchy and Poisson transforms for commuting families of row contractions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poisson transforms on right-angled Artin monoids Li, Boyu Operator Algebras Functional Analysis 47A13, 47A20, 47D03 We introduce the notion of the weak Brehmer's condition and prove that the Cauchy transform for a representation of a right-angled Artin monoid is bounded under such conditions. As a result, we obtain the Poisson transform and $*$-regular dilation for a family of operators that satisfies the weak Brehmer's condition and the property (P). This generalizes Popescu's notion of Cauchy and Poisson transforms for commuting families of row contractions. |
| title | Poisson transforms on right-angled Artin monoids |
| topic | Operator Algebras Functional Analysis 47A13, 47A20, 47D03 |
| url | https://arxiv.org/abs/2504.00127 |